Optical astronomy is increasingly concerned with the detection of faint companions, which may eventually include planetary systems, close to much brighter primary stars. Detection limits are generally set by "speckle noise," random variations in focal plane intensity that result when atmospheric turbulence redistributes the undesirably copious flux of the primary. It is well known that adaptive optics (AO) reduces the fraction of light diverted into speckles. But at a moderately high Strehl ratio, additional effects become important, including anomalous bright speckles that may have negative intensity and that are "pinned" on the secondary maxima of the diffraction-limited point-spread function (PSF). I show that companion-detection sensitivity is noticeably better on Airy nulls, even at current AO performance levels. I also show that future high adaptive correction may give regimes in which speckle noise, dominated by these anomalous speckles, has zero mean and cancels instantaneously over a detector on a PSF null to a zero that is "regulated" against seeing or correction fluctuations.